Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function

1.

2.

Warm – up #8

1.

V (2, 4)Axis of Symmetry: x = 2

Right 2 Up 4Reflect over x-axis

Warm – up #8 Solutions

2.

V (0, -7)

Axis of Symmetry: x = 0

Down 7Reflect over x-axis

Reflect over y-axis -x

Warm – up #8 Solutions

Homework Log

Fri

10/2

Lesson 2 – 8

Learning Objective: To graph two variable inequalities

Hw: Pg. 118 #8 – 17, 39 – 41, *46

10/2/15 Lesson 2 – 8 Two Variable Inequalities

Algebra II

To graph two variable inequalities

Learning Objective

Linear Inequality – an inequality in two variables (x & y) whose graph is the region of the coordinate plane bounded (stopped) by a line

Boundary – line that bounds the graph of a linear inequality

Test Point – a point not on the boundary. Use it to check whether the point satisfies the inequality. Usually (0, 0)

If it satisfies the inequality, shade the side of the line containing that point

If it does not satisfy the inequality, shade the other side of the line that does not contain the point.

1. y > 3x – 1dotted line!

Check (0, 0)0 > 3(0) – 10 > 0 – 10 > -1 TRUE!Shade side with

(0, 0)

Graph Linear Inequality

2. y -2x + 1solid line!

Check (0, 0)0 -2(0) + 10 0 + 10 + 1 FALSE!Shade side withOUT

(0, 0)

Graph Linear Inequality

Shade above the liney dottedy solid

Shade below the liney dottedy solid

Trick

3. y < -x + 3dotted lineShade belowCheck (0, 0)0 < -0 + 30 < 0 + 30 < 3 TRUE!Shade side with

(0, 0)

Graph Linear Inequality

4. y x +1solid lineShade aboveCheck (0, 0)0 + 10 0 + 10 FALSE!Shade side without

(0, 0)

Graph Linear Inequality

5. y -2 dotted lineShade below

Check (0, 0)0 < -2 FALSE!Shade side withOUT

(0, 0)

Graph Linear Inequality

6. x -3 solid line

Check (0, 0)0 -3 TRUE!Shade side with

(0, 0)

Graph Linear Inequality

7. The equation for the boundary line is x – 3y = 15

x – 3y = 15-x -x-3y = -x + 15 -3 -3 -3

y - 5

Write an inequality for the graph

¿

8. (0, -4) & (-5, 0)

y

8. Write an inequality for the graph

¿

8. (0, -2) & (1, 0)

y

9. Write an inequality for the graph

≥

8. (0, 4) & (3, -3)

y

10. Write an inequality for the graph

¿

When you graph an inequality, you can often use the point (0, 0) to test which side of the boundary to shade. Describe a situation in which you could not use (0, 0) as a test point.

Ticket Out the Door

Assignment:

Pg. 118 #8 – 17, 39 – 41, *46